This application has three major aims that exploit the use of mathematical programming tools for biophysically motivated problems. The first goal is the refinement of protein structures that are obtained from homology. Structures based on homology are rarely of atomic resolution;a resolution which is necessary for detailed modeling of protein function, and for the design of drug molecules. Based on mathematical programming approach a new class of energy functions, suitable for the refinement problem, will be designed. The second goal is to investigate a new type of network;the network of sequence flow between protein structures. We examine the process in which new sequences, generated by point mutations, remain in the current fold, or switch to other stable structures (we exclude sequences with no stable fold). The adjustments to the structure are accepted or rejected based on stability criterion. The net. work defines a master equation which makes it possible to investigate past (ancient) folds, and future structures that serve as attractors. The third aim examines the network of protein-protein (physical) interactions and will be examined with bioinformatics and biophysical approaches. Comparison will be made between the network of sequence flow and the network of protein-protein interactions to better understand the evolution of biological mechanisms and recognition. PUBLIC HEALTH RELEVANCE The design of new algorithms to predict protein structures and protein-protein interactions is likely to help with the design of new drug molecules.